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Answer :
To find the percent yield of silver in the reaction between copper metal and silver nitrate, we can follow these steps:
1. Understand the Reaction:
The chemical reaction given is:
[tex]\( \text{Cu} + 2 \text{AgNO}_3 \rightarrow \text{Cu(NO}_3\text{)}_2 + 2 \text{Ag} \)[/tex]
This tells us one mole of copper reacts with two moles of silver nitrate to produce two moles of silver.
2. Calculate Moles of Copper Used:
We start with 12.7 grams of copper. To find the moles of copper, use its molar mass.
- Molar mass of copper (Cu) = 63.55 g/mol
[tex]\[
\text{Moles of Cu} = \frac{12.7 \text{ g}}{63.55 \text{ g/mol}} = 0.19984 \text{ moles}
\][/tex]
3. Determine Moles of Silver Expected:
According to the reaction stoichiometry, 1 mole of copper produces 2 moles of silver.
[tex]\[
\text{Moles of Ag expected} = 2 \times 0.19984 \text{ moles of Cu} = 0.39968 \text{ moles of Ag}
\][/tex]
4. Calculate Mass of Silver Expected:
Use the molar mass of silver to find the expected mass of silver.
- Molar mass of silver (Ag) = 107.87 g/mol
[tex]\[
\text{Mass of Ag expected} = 0.39968 \text{ moles} \times 107.87 \text{ g/mol} = 43.11 \text{ grams}
\][/tex]
5. Calculate Percent Yield:
Percent yield is determined using the actual mass of silver produced and the expected mass.
[tex]\[
\text{Percent yield} = \left(\frac{\text{Actual mass of Ag produced}}{\text{Mass of Ag expected}}\right) \times 100
\][/tex]
[tex]\[
\text{Percent yield} = \left(\frac{38.1 \text{ g}}{43.11 \text{ g}}\right) \times 100 = 88.4\%
\][/tex]
Therefore, the percent yield of silver in this reaction is approximately 88.4%. This result matches one of the given options, confirming its accuracy.
1. Understand the Reaction:
The chemical reaction given is:
[tex]\( \text{Cu} + 2 \text{AgNO}_3 \rightarrow \text{Cu(NO}_3\text{)}_2 + 2 \text{Ag} \)[/tex]
This tells us one mole of copper reacts with two moles of silver nitrate to produce two moles of silver.
2. Calculate Moles of Copper Used:
We start with 12.7 grams of copper. To find the moles of copper, use its molar mass.
- Molar mass of copper (Cu) = 63.55 g/mol
[tex]\[
\text{Moles of Cu} = \frac{12.7 \text{ g}}{63.55 \text{ g/mol}} = 0.19984 \text{ moles}
\][/tex]
3. Determine Moles of Silver Expected:
According to the reaction stoichiometry, 1 mole of copper produces 2 moles of silver.
[tex]\[
\text{Moles of Ag expected} = 2 \times 0.19984 \text{ moles of Cu} = 0.39968 \text{ moles of Ag}
\][/tex]
4. Calculate Mass of Silver Expected:
Use the molar mass of silver to find the expected mass of silver.
- Molar mass of silver (Ag) = 107.87 g/mol
[tex]\[
\text{Mass of Ag expected} = 0.39968 \text{ moles} \times 107.87 \text{ g/mol} = 43.11 \text{ grams}
\][/tex]
5. Calculate Percent Yield:
Percent yield is determined using the actual mass of silver produced and the expected mass.
[tex]\[
\text{Percent yield} = \left(\frac{\text{Actual mass of Ag produced}}{\text{Mass of Ag expected}}\right) \times 100
\][/tex]
[tex]\[
\text{Percent yield} = \left(\frac{38.1 \text{ g}}{43.11 \text{ g}}\right) \times 100 = 88.4\%
\][/tex]
Therefore, the percent yield of silver in this reaction is approximately 88.4%. This result matches one of the given options, confirming its accuracy.
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